Question: Solve for $x$. Enter the solutions from least to greatest. $(x -4)(-5x +1)=0$ $\text{lesser }x = $
Explanation: For any two expressions $A$ and $B$ : If $A\cdot B=0$ then either $A=0$ or $B=0$. This is called the zero product property. In our case, $(x -4)(-5x +1)=0$. So either $(x -4)=0$ or $(-5x +1)=0$ : $\begin{aligned} (1)&&x -4&=0 \\\\ &&x&=4 \end{aligned}$ $\begin{aligned} (2)&&-5x +1&=0 \\\\ &&-5x &= -1 \\\\ &&x&=\dfrac{1}{5} \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= \dfrac{1}{5} \\\\ \text{greater } x &= 4 \end{aligned}$